Solved on Jan 23, 2024

Simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ .

STEP 1

Assumptions
1. We need to simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ using the order of operations.
2. The order of operations is parentheses, exponents, multiplication, and division from left to right.

STEP 2

First, we need to simplify the exponentiation part of the expression.
$\left(\frac{4}{25}\right)^{2}$

STEP 3

Calculate the square of the fraction by squaring both the numerator and the denominator.
$\left(\frac{4}{25}\right)^{2} = \frac{4^2}{25^2}$

STEP 4

Compute the squares of 4 and 25.
$\frac{4^2}{25^2} = \frac{16}{625}$

STEP 5

Next, we simplify the exponentiation part for $2^{4}$ .
$2^{4} = 2 \times 2 \times 2 \times 2$

STEP 6

Calculate the value of $2^{4}$ .
$2^{4} = 16$

STEP 7

Now, we have two parts of the expression simplified:
$\frac{16}{625} \text{ and } 16$
We will multiply these two parts together.

STEP 8

Multiply the simplified fraction by the power of 2.
$\frac{16}{625} \times 16$

STEP 9

Multiply the numerators and keep the denominator the same.
$\frac{16 \times 16}{625}$

STEP 10

Calculate the product of the numerators.
$\frac{256}{625}$

STEP 11

Now we need to simplify the division part of the expression:
$\div\left(\frac{15}{2}\right)$

STEP 12

Dividing by a fraction is the same as multiplying by its reciprocal.
$\frac{256}{625} \times \frac{2}{15}$

STEP 13

Multiply the numerators and the denominators.
$\frac{256 \times 2}{625 \times 15}$

STEP 14

Calculate the product of the numerators and the product of the denominators.
$\frac{512}{9375}$

STEP 15

Now, we need to simplify the fraction if possible.

STEP 16

Check if there is a common factor between the numerator and the denominator.

STEP 17

Since 512 and 9375 do not share any common factors other than 1, the fraction is already in its simplest form.
The simplified expression is:
$\frac{512}{9375}$

Was this helpful?

Simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ .

STEP 1

Assumptions
1. We need to simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ using the order of operations.
2. The order of operations is parentheses, exponents, multiplication, and division from left to right.

STEP 2

First, we need to simplify the exponentiation part of the expression.
$\left(\frac{4}{25}\right)^{2}$

STEP 3

Calculate the square of the fraction by squaring both the numerator and the denominator.
$\left(\frac{4}{25}\right)^{2} = \frac{4^2}{25^2}$

STEP 4

Compute the squares of 4 and 25.
$\frac{4^2}{25^2} = \frac{16}{625}$

STEP 5

Next, we simplify the exponentiation part for $2^{4}$ .
$2^{4} = 2 \times 2 \times 2 \times 2$

STEP 6

Calculate the value of $2^{4}$ .
$2^{4} = 16$

STEP 7

Now, we have two parts of the expression simplified:
$\frac{16}{625} \text{ and } 16$
We will multiply these two parts together.

STEP 8

Multiply the simplified fraction by the power of 2.
$\frac{16}{625} \times 16$

STEP 9

Multiply the numerators and keep the denominator the same.
$\frac{16 \times 16}{625}$

STEP 10

Calculate the product of the numerators.
$\frac{256}{625}$

STEP 11

Now we need to simplify the division part of the expression:
$\div\left(\frac{15}{2}\right)$

STEP 12

Dividing by a fraction is the same as multiplying by its reciprocal.
$\frac{256}{625} \times \frac{2}{15}$

STEP 13

Multiply the numerators and the denominators.
$\frac{256 \times 2}{625 \times 15}$

STEP 14

Calculate the product of the numerators and the product of the denominators.
$\frac{512}{9375}$

STEP 15

Now, we need to simplify the fraction if possible.

STEP 16

Check if there is a common factor between the numerator and the denominator.

STEP 17

Since 512 and 9375 do not share any common factors other than 1, the fraction is already in its simplest form.
The simplified expression is:
$\frac{512}{9375}$

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Simplify the expression (425)2×24÷(152)\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)(254​)2×24÷(215​).

STEP 1

Assumptions1. We need to simplify the expression (425)2×24÷(152)\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)(254​)2×24÷(215​) using the order of operations.2. The order of operations is parentheses, exponents, multiplication, and division from left to right.

STEP 2

First, we need to simplify the exponentiation part of the expression.(425)2\left(\frac{4}{25}\right)^{2}(254​)2

STEP 3

Calculate the square of the fraction by squaring both the numerator and the denominator.(425)2=42252\left(\frac{4}{25}\right)^{2} = \frac{4^2}{25^2}(254​)2=25242​

STEP 4

Compute the squares of 4 and 25.42252=16625\frac{4^2}{25^2} = \frac{16}{625}25242​=62516​

STEP 5

Next, we simplify the exponentiation part for 242^{4}24.24=2×2×2×22^{4} = 2 \times 2 \times 2 \times 224=2×2×2×2

STEP 6

Calculate the value of 242^{4}24.24=162^{4} = 1624=16

STEP 7

Now, we have two parts of the expression simplified:16625 and 16\frac{16}{625} \text{ and } 1662516​ and 16We will multiply these two parts together.

STEP 8

Multiply the simplified fraction by the power of 2.16625×16\frac{16}{625} \times 1662516​×16

STEP 9

Multiply the numerators and keep the denominator the same.16×16625\frac{16 \times 16}{625}62516×16​

STEP 10

Calculate the product of the numerators.256625\frac{256}{625}625256​

STEP 11

Now we need to simplify the division part of the expression:÷(152)\div\left(\frac{15}{2}\right)÷(215​)

STEP 12

Dividing by a fraction is the same as multiplying by its reciprocal.256625×215\frac{256}{625} \times \frac{2}{15}625256​×152​

STEP 13

Multiply the numerators and the denominators.256×2625×15\frac{256 \times 2}{625 \times 15}625×15256×2​

STEP 14

Calculate the product of the numerators and the product of the denominators.5129375\frac{512}{9375}9375512​

STEP 15

Now, we need to simplify the fraction if possible.

STEP 16

Check if there is a common factor between the numerator and the denominator.

STEP 17

Since 512 and 9375 do not share any common factors other than 1, the fraction is already in its simplest form.The simplified expression is:5129375\frac{512}{9375}9375512​

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ .

Assumptions
1. We need to simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ using the order of operations.
2. The order of operations is parentheses, exponents, multiplication, and division from left to right.

First, we need to simplify the exponentiation part of the expression.
$\left(\frac{4}{25}\right)^{2}$

Calculate the square of the fraction by squaring both the numerator and the denominator.
$\left(\frac{4}{25}\right)^{2} = \frac{4^2}{25^2}$

Compute the squares of 4 and 25.
$\frac{4^2}{25^2} = \frac{16}{625}$

Next, we simplify the exponentiation part for $2^{4}$ .
$2^{4} = 2 \times 2 \times 2 \times 2$

Calculate the value of $2^{4}$ .
$2^{4} = 16$

Now, we have two parts of the expression simplified:
$\frac{16}{625} \text{ and } 16$
We will multiply these two parts together.

Multiply the simplified fraction by the power of 2.
$\frac{16}{625} \times 16$

Multiply the numerators and keep the denominator the same.
$\frac{16 \times 16}{625}$

Calculate the product of the numerators.
$\frac{256}{625}$

Now we need to simplify the division part of the expression:
$\div\left(\frac{15}{2}\right)$

Dividing by a fraction is the same as multiplying by its reciprocal.
$\frac{256}{625} \times \frac{2}{15}$

Multiply the numerators and the denominators.
$\frac{256 \times 2}{625 \times 15}$

Calculate the product of the numerators and the product of the denominators.
$\frac{512}{9375}$

Since 512 and 9375 do not share any common factors other than 1, the fraction is already in its simplest form.
The simplified expression is:
$\frac{512}{9375}$