Solved on Feb 13, 2024

Rewrite the equation $y = \frac{9}{4x^5}$ to not be a fraction.

STEP 1

Assumptions
1. The equation given is $y = \frac{9}{4x^5}$ .
2. We want to rewrite the equation so that it is not in fractional form.

STEP 2

To rewrite the equation without a fraction, we can use the property of negative exponents, which states that $a^{-n} = \frac{1}{a^n}$ .

STEP 3

Apply the property of negative exponents to the denominator of the fraction.
$y = 9 \cdot (4x^5)^{-1}$

STEP 4

Distribute the negative exponent to both the coefficient and the variable part of the denominator.
$y = 9 \cdot 4^{-1} \cdot (x^5)^{-1}$

STEP 5

Simplify the expression by calculating $4^{-1}$ and writing $(x^5)^{-1}$ as $x^{-5}$ .
$y = 9 \cdot \frac{1}{4} \cdot x^{-5}$

STEP 6

Combine the constant terms to complete the rewriting of the equation.
$y = \frac{9}{4} \cdot x^{-5}$
The equation rewritten without a fraction is $y = \frac{9}{4} \cdot x^{-5}$ .

Was this helpful?

Rewrite the equation $y = \frac{9}{4x^5}$ to not be a fraction.

STEP 1

Assumptions
1. The equation given is $y = \frac{9}{4x^5}$ .
2. We want to rewrite the equation so that it is not in fractional form.

STEP 2

To rewrite the equation without a fraction, we can use the property of negative exponents, which states that $a^{-n} = \frac{1}{a^n}$ .

STEP 3

Apply the property of negative exponents to the denominator of the fraction.
$y = 9 \cdot (4x^5)^{-1}$

STEP 4

Distribute the negative exponent to both the coefficient and the variable part of the denominator.
$y = 9 \cdot 4^{-1} \cdot (x^5)^{-1}$

STEP 5

Simplify the expression by calculating $4^{-1}$ and writing $(x^5)^{-1}$ as $x^{-5}$ .
$y = 9 \cdot \frac{1}{4} \cdot x^{-5}$

STEP 6

Combine the constant terms to complete the rewriting of the equation.
$y = \frac{9}{4} \cdot x^{-5}$
The equation rewritten without a fraction is $y = \frac{9}{4} \cdot x^{-5}$ .

Start learning now

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

Rewrite the equation y=94x5y = \frac{9}{4x^5}y=4x59​ to not be a fraction.

STEP 1

Assumptions1. The equation given is y=94x5 y = \frac{9}{4x^5} y=4x59​.2. We want to rewrite the equation so that it is not in fractional form.

STEP 2

To rewrite the equation without a fraction, we can use the property of negative exponents, which states that a−n=1an a^{-n} = \frac{1}{a^n} a−n=an1​.

STEP 3

Apply the property of negative exponents to the denominator of the fraction.y=9⋅(4x5)−1 y = 9 \cdot (4x^5)^{-1} y=9⋅(4x5)−1

STEP 4

Distribute the negative exponent to both the coefficient and the variable part of the denominator.y=9⋅4−1⋅(x5)−1 y = 9 \cdot 4^{-1} \cdot (x^5)^{-1} y=9⋅4−1⋅(x5)−1

STEP 5

Simplify the expression by calculating 4−1 4^{-1} 4−1 and writing (x5)−1 (x^5)^{-1} (x5)−1 as x−5 x^{-5} x−5.y=9⋅14⋅x−5 y = 9 \cdot \frac{1}{4} \cdot x^{-5} y=9⋅41​⋅x−5

STEP 6

Combine the constant terms to complete the rewriting of the equation.y=94⋅x−5 y = \frac{9}{4} \cdot x^{-5} y=49​⋅x−5The equation rewritten without a fraction is y=94⋅x−5 y = \frac{9}{4} \cdot x^{-5} y=49​⋅x−5.

Start learning now

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

Rewrite the equation $y = \frac{9}{4x^5}$ to not be a fraction.

Assumptions
1. The equation given is $y = \frac{9}{4x^5}$ .
2. We want to rewrite the equation so that it is not in fractional form.

To rewrite the equation without a fraction, we can use the property of negative exponents, which states that $a^{-n} = \frac{1}{a^n}$ .

Apply the property of negative exponents to the denominator of the fraction.
$y = 9 \cdot (4x^5)^{-1}$

Distribute the negative exponent to both the coefficient and the variable part of the denominator.
$y = 9 \cdot 4^{-1} \cdot (x^5)^{-1}$

Simplify the expression by calculating $4^{-1}$ and writing $(x^5)^{-1}$ as $x^{-5}$ .
$y = 9 \cdot \frac{1}{4} \cdot x^{-5}$

Combine the constant terms to complete the rewriting of the equation.
$y = \frac{9}{4} \cdot x^{-5}$
The equation rewritten without a fraction is $y = \frac{9}{4} \cdot x^{-5}$ .