Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select the equivalent expression.

(6^(-4)*8^(-7))^(-9)=?
Choose 1 answer:
(A)
(1)/(6^(13)*8^(16))
(B)
6^(36)*8^(63)
(C)
6^(5)*8^(2)

Select the equivalent expression. $\newline$ $(6^{-4}\cdot8^{-7})^{-9}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{6^{13}\cdot8^{16}}$ $\newline$ (B) $6^{36}\cdot8^{63}$ $\newline$ (C) $6^{5}\cdot8^{2}$

View step-by-step help

View step-by-step help

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(6^{-4}\cdot8^{-7})^{-9}=

?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{6^{13}\cdot8^{16}}

\newline

(B)

6^{36}\cdot8^{63}

\newline

(C)

6^{5}\cdot8^{2}

Calculate new exponents: Now, we calculate the new exponents by multiplying the inner and outer exponents for both bases. $\newline$ For $6^{-4}$ , we have $(-4) \times (-9) = 36$ . $\newline$ For $8^{-7}$ , we have $(-7) \times (-9) = 63$ . $\newline$ So, $(6^{-4})^{-9} = 6^{36}$ and $(8^{-7})^{-9} = 8^{63}$ .
Combine the results: Next, we combine the results to get the equivalent expression. $\newline$ $(6^{-4}\cdot8^{-7})^{-9} = 6^{36} \cdot 8^{63}$ .
Match the answer choices: We now look at the answer choices to see which one matches our result. $\newline$ (A) $(1)/(6^{13}*8^{16})$ does not match our result. $\newline$ (B) $6^{36}*8^{63}$ matches our result. $\newline$ (C) $6^{5}*8^{2}$ does not match our result.
Correct answer: Therefore, the correct answer is $(B) 6^{36}\cdot8^{63}$ .

More problems from Evaluate expressions using properties of exponents

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 2 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 2 months ago

Question

x^2 = 4

Posted 1 month ago

Question

x^2 = 9

Posted 3 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 3 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 3 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 3 months ago

Question

Select the equivalent expression.

\newline

((8^{-5})/(2^{-2}))^{-4}=?

\newline

1

\newline

\newline

(8^{20})/(2^{8})

\newline

\newline

(2^{6})/(8^{9})

\newline

\newline

(1)/(8\cdot 2^{2})

Posted 4 days ago

Question

Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?

\newline

1

\newline

\frac{b^{21}}{4^{15}}

\newline

\frac{4^{15}}{b^{21}}

\newline

b^{-21}\cdot 4^{-15}

Posted 1 month ago

Question

Select the equivalent expression.

\newline

(3^{3}\cdot6^{6})^{-3}=

\newline

1

\newline

\frac{1}{3^{9}\cdot6^{18}}

\newline

\frac{6^{18}}{3^{9}}

\newline

\frac{3^{9}}{6^{18}}

Posted 1 month ago