QuestionWhich expression equals $4^{5} \times 4^{-7} \div 4^{-2}$ ? Choices: $4^{-4}$ , $4^{5} \div 4^{-9}$ , $4^{0}$ .

Studdy Solution

STEP 1

Assumptions1. The base of all the expressions is4. The laws of exponents apply, which are a. $a^{m} \times a^{n} = a^{m+n}$ b. $\frac{a^{m}}{a^{n}} = a^{m-n}$ c. $a^{-n} = \frac{1}{a^{n}}$

STEP 2

We start by simplifying the given expression using the laws of exponents. The expression is $4^{5} \times4^{-7} \div4^{-2}$ .

STEP 3

First, we can simplify the multiplication and division operations using the laws of exponents. According to the law $a^{m} \times a^{n} = a^{m+n}$ and $\frac{a^{m}}{a^{n}} = a^{m-n}$ , we can add the exponents when multiplying and subtract the exponents when dividing.
$^{5} \times^{-7} \div^{-2} =^{5 + (-7) - (-2)}$

STEP 4

implify the expression inside the parentheses.
$4^{ + (-7) - (-2)} =4^{ -7 +2}$

STEP 5

Perform the operations inside the parentheses.
$4^{5 -7 +2} =4^{0}$

STEP 6

By the law of exponents, any number raised to the power of0 is1. Therefore, the expression simplifies to1.
$4^{0} =1$ Therefore, the expression $4^{5} \times4^{-} \div4^{-2}$ is equal to $4^{0}$ .

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QuestionWhich expression equals $4^{5} \times 4^{-7} \div 4^{-2}$ ? Choices: $4^{-4}$ , $4^{5} \div 4^{-9}$ , $4^{0}$ .

Studdy Solution

STEP 1

Assumptions1. The base of all the expressions is4. The laws of exponents apply, which are a. $a^{m} \times a^{n} = a^{m+n}$ b. $\frac{a^{m}}{a^{n}} = a^{m-n}$ c. $a^{-n} = \frac{1}{a^{n}}$

STEP 2

We start by simplifying the given expression using the laws of exponents. The expression is $4^{5} \times4^{-7} \div4^{-2}$ .

STEP 3

STEP 4

implify the expression inside the parentheses.
$4^{ + (-7) - (-2)} =4^{ -7 +2}$

STEP 5

Perform the operations inside the parentheses.
$4^{5 -7 +2} =4^{0}$

STEP 6

By the law of exponents, any number raised to the power of0 is1. Therefore, the expression simplifies to1.
$4^{0} =1$ Therefore, the expression $4^{5} \times4^{-} \div4^{-2}$ is equal to $4^{0}$ .

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QuestionWhich expression equals 45×4−7÷4−24^{5} \times 4^{-7} \div 4^{-2}45×4−7÷4−2? Choices: 4−44^{-4}4−4, 45÷4−94^{5} \div 4^{-9}45÷4−9, 404^{0}40.

Studdy Solution

STEP 1

Assumptions1. The base of all the expressions is4. The laws of exponents apply, which are a. am×an=am+na^{m} \times a^{n} = a^{m+n}am×an=am+n b. aman=am−n\frac{a^{m}}{a^{n}} = a^{m-n}anam​=am−n c. a−n=1ana^{-n} = \frac{1}{a^{n}}a−n=an1​

STEP 2

We start by simplifying the given expression using the laws of exponents. The expression is 45×4−7÷4−24^{5} \times4^{-7} \div4^{-2}45×4−7÷4−2.

STEP 3

STEP 4

implify the expression inside the parentheses.4+(−7)−(−2)=4−7+24^{ + (-7) - (-2)} =4^{ -7 +2}4+(−7)−(−2)=4−7+2

STEP 5

Perform the operations inside the parentheses.45−7+2=404^{5 -7 +2} =4^{0}45−7+2=40

STEP 6

By the law of exponents, any number raised to the power of0 is1. Therefore, the expression simplifies to1.40=14^{0} =140=1Therefore, the expression 45×4−÷4−24^{5} \times4^{-} \div4^{-2}45×4−÷4−2 is equal to 404^{0}40.

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QuestionWhich expression equals $4^{5} \times 4^{-7} \div 4^{-2}$ ? Choices: $4^{-4}$ , $4^{5} \div 4^{-9}$ , $4^{0}$ .

Assumptions1. The base of all the expressions is4. The laws of exponents apply, which are a. $a^{m} \times a^{n} = a^{m+n}$ b. $\frac{a^{m}}{a^{n}} = a^{m-n}$ c. $a^{-n} = \frac{1}{a^{n}}$

We start by simplifying the given expression using the laws of exponents. The expression is $4^{5} \times4^{-7} \div4^{-2}$ .

implify the expression inside the parentheses.
$4^{ + (-7) - (-2)} =4^{ -7 +2}$

Perform the operations inside the parentheses.
$4^{5 -7 +2} =4^{0}$

By the law of exponents, any number raised to the power of0 is1. Therefore, the expression simplifies to1.
$4^{0} =1$ Therefore, the expression $4^{5} \times4^{-} \div4^{-2}$ is equal to $4^{0}$ .