Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Evaluate.
32^((-3)/(5))=2^◻

Evaluate. $\newline$ $32^{\frac{-3}{5}}=2^{\square}$

View step-by-step help

View step-by-step help

Powers with negative bases

Full solution

Q. Evaluate.

\newline

32^{\frac{-3}{5}}=2^{\square}

Evaluate Base: Evaluate the base of the exponent to see if it can be related to the exponent's form. $\newline$ $32$ is a power of $2$ , specifically $2^5$ , since $2 \times 2 \times 2 \times 2 \times 2 = 32$ .
Rewrite Expression: Rewrite the expression using the base of $2$ . $32^{(-3)/(5)}$ can be written as $(2^5)^{(-3)/(5)}$ .
Apply Power Rule: Apply the power of a power rule, which states that a^b)^c = a^{(b*c)}\. \(\(2^ $5$ )^{( $-3$ )/( $5$ )}\ becomes (2\)^{( $5$ * ( $-3$ )/( $5$ ))}\.
Simplify Exponent: Simplify the exponent by multiplying $5$ by $-\frac{3}{5}$ . $5 \times \left(-\frac{3}{5}\right) = -3$ .
Negative Exponent: Now the expression is $2^{-3}$ . $\newline$ To simplify a negative exponent, recall that $a^{-n} = \frac{1}{a^n}$ . $\newline$ $2^{-3} = \frac{1}{2^3}.$
Calculate Value: Calculate $2^3$ . $2^3 = 2 \times 2 \times 2 = 8$ .
Substitute Back: Substitute the value back into the expression. $\newline$ $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$ .

More problems from Powers with negative bases

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 5 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