Match each algebraic expression with its simplified equivalent form.

$x^3 \cdot x^2$ $x^5$
$\frac{x^8}{x^2}$ $x^6$
$(x^4)^2$ $x^8$
$x^{-3}$ $\frac{1}{x^3}$

Answer

The matches are:

x^3 \cdot x^2

simplifies to

x^5

\frac{x^8}{x^2}

simplifies to

x^6

(x^4)^2

simplifies to

x^8

, and

x^{-3}

simplifies to

\frac{1}{x^3}

Each expression correctly pairs with its simplified form by applying the four fundamental rules of exponents: the product rule, the quotient rule, the power of a power rule, and the negative exponent rule.

Step-by-Step Solution

Apply the product rule for exponents to

x^3 \cdot x^2

x^{3+2} = x^5

Multiplying identical bases requires adding the exponents.

Apply the quotient rule for exponents to

\frac{x^8}{x^2}

x^{8-2} = x^6

Dividing identical bases requires subtracting the denominator's exponent.

Apply the power rule for exponents to

(x^4)^2

x^{4 \cdot 2} = x^8

Raising an exponent to another power requires multiplying the exponents.

Apply the negative exponent rule to

x^{-3}

\frac{1}{x^3}

A negative exponent signifies the reciprocal of the corresponding positive exponent.

Key Concept

Operations with Variable Exponents

Estimated Time:1m 0s

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