Select the equivalent expression. (x^(5)*x^(5))/(x^(6)) (1)/(x^(6)) x^(6) x^(4) (1)/(x^(4))

Apply Exponent Rule: Apply the exponent rule for multiplication, which states that when you multiply two powers with the same base, you add the exponents. So, x^(5) * x^(5) becomes x^(5+5). Calculation: 5 + 5 = 10 Therefore, x^(5) * x^(5) = x^(10).Divide by Exponent Rule: Now, divide the result by x^(6) using the exponent rule for division, which states that when you divide two powers with the same base, you subtract the exponents. So, x^(10) / x^(6) becomes x^(10-6). Calculation: 10 - 6 = 4 Therefore, x^(10) / x^(6) = x^(4).Check Answer Choices: Check the answer choices to see which one matches the result from Step 2. The correct answer is x^(4).

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Select the equivalent expression.

(x^(5)*x^(5))/(x^(6))

(1)/(x^(6))

x^(6)

x^(4)

(1)/(x^(4))

Select the equivalent expression. $\newline$ $\frac{x^{5} \cdot x^{5}}{x^{6}}$ $\newline$ $\frac{1}{x^{6}}$ $\newline$ $x^{6}$ $\newline$ $x^{4}$ $\newline$ $\frac{1}{x^{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{5} \cdot x^{5}}{x^{6}}

\newline

\frac{1}{x^{6}}

\newline

x^{6}

\newline

x^{4}

\newline

\frac{1}{x^{4}}

Apply Exponent Rule: Apply the exponent rule for multiplication, which states that when you multiply two powers with the same base, you add the exponents. $\newline$ So, $x^{5} \times x^{5}$ becomes $x^{5+5}$ . $\newline$ Calculation: $5 + 5 = 10$ $\newline$ Therefore, $x^{5} \times x^{5} = x^{10}$ .
Divide by Exponent Rule: Now, divide the result by $x^{(6)}$ using the exponent rule for division, which states that when you divide two powers with the same base, you subtract the exponents. $\newline$ So, $x^{(10)} / x^{(6)}$ becomes $x^{(10-6)}$ . $\newline$ Calculation: $10 - 6 = 4$ $\newline$ Therefore, $x^{(10)} / x^{(6)} = x^{4}$ .
Check Answer Choices: Check the answer choices to see which one matches the result from Step $2$ . $\newline$ The correct answer is $x^{4}$ .