Question
Write \( x^{2} \cdot x^{3} \) without exponents \[ x^{2} \cdot x^{5}=\prod \]
Ask by Greene Lambert. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2} \cdot x^{3} = x \cdot x \cdot x \cdot x \)
Solution
When multiplying powers with the same base, you add the exponents.
For the first expression:
x² · x³ = x^(2+3) = x⁵.
Writing x⁵ without using exponents means multiplying x by itself five times:
x⁵ = x · x · x · x · x.
Similarly, for the second expression provided:
x² · x⁵ = x^(2+5) = x⁷.
And written without exponents, x⁷ is:
x⁷ = x · x · x · x · x · x · x.
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Simplify this solution Beyond the Answer
To express \( x^{2} \cdot x^{3} \) without exponents, you simply multiply the bases together by adding the exponents. So, \( x^{2} \cdot x^{3} = x^{2+3} = x^{5} \). Now, for \( x^{2} \cdot x^{5} \): Following the same rule, you add the exponents \( 2 + 5 = 7 \). Therefore, \( x^{2} \cdot x^{5} = x^{7} \). In the product notation: \[ x^{2} \cdot x^{5} = x^{7} \] or \[ \prod = x^7 \] (since \(\prod\) signifies the product).
