Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer using positive exponents. $\newline$ $a^{-2} \times a^{5} \times a^{-5}$

View step-by-step help

View step-by-step help

Simplify exponential expressions using exponent rules

Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

a^{-2} \times a^{5} \times a^{-5}

Identify Operation: $a^{-2} \times a^{5} \times a^{-5}$ $\newline$ What operation is needed for the exponents $-2$ , $5$ , and $-5$ ?
Combine Exponents: $a^{-2} \times a^{5} \times a^{-5}$ $\newline$ Rewrite this expression as a single power of $a$ . $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $a^{-2} \times a^{5} \times a^{-5}$ $\newline$ = $a^{(-2 + 5 + (-5))}$ $\newline$ = $a^{-2}$
Convert to Positive Exponent: $a^{-2}$ $\newline$ Since the question prompt asks for positive exponents, we need to express $a^{-2}$ with a positive exponent. $\newline$ We know that $a^{-n} = \frac{1}{a^n}$ for any positive integer $n$ . $\newline$ Therefore, $a^{-2} = \frac{1}{a^2}$ .

More problems from Simplify exponential expressions using exponent rules

Question

Order the expressions from least to greatest.

\newline

5^{2} \quad 4^{2}+2^{2} \quad 6^{2}-6

Posted 1 year ago

Question

Evaluate the expression. Do not round your answer.

\newline

\frac{1}{5}(3+2+5)^{2}=

Posted 1 year ago

Question

Evaluate the expression.

\newline

Do not round your answer.

\newline

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

Posted 1 year ago

Question

Evaluate the following expression.

\newline

8^{3}-9 \cdot 2 \div 3=

Posted 1 year ago

Question

Evaluate the expression. Do not round your answer.

\newline

\frac{1}{4}(6+3+1)^{2}=

Posted 1 year ago

Question

Evaluate the expression. Do not round your answer.

\newline

(2 \cdot 3)^{2}+5^{2}=

Posted 1 year ago

Question

Evaluate the expression. Do not round your answer.

\newline

\frac{1}{3}(4 \cdot 3)+2^{3}=

Posted 1 year ago

Question

Evaluate the expression.

\newline

Do not round your answer.

\newline

2\left(3^{2}+4^{2}\right)=

Posted 1 year ago

Question

\newline

2 \times 10-7 \times 2=

Posted 1 year ago

Question

-1.2-\frac{29}{20}=

\newline

Enter the answer as an exact decimal or simplified fraction.

Posted 11 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant