solve the exponential equation $\\sqrt{a} \\cdot \\sqrt{a} \\cdot a^3 =…

solve the exponential equation $\\sqrt{a} \\cdot \\sqrt{a} \\cdot a^3 = a^x$ for x.
options:
x equals 3
x equals 2
x equals $\\frac{2}{3}$
x equals 4

Understand the question
solve the exponential equation $\\sqrt{a} \\cdot \\sqrt{a} \\cdot a^3 = a^x$ for x.
options:
x equals 3
x equals 2
x equals $\\frac{2}{3}$
x equals 4
Explanation
Step1: Rewrite root as exponent

$\sqrt{a} = a^\frac{1}{2}$

Step2: Substitute into left-hand side

$a^\frac{1}{2} \cdot a^\frac{1}{2} \cdot a^3$

Step3: Add exponents (same base)

$\frac{1}{2} + \frac{1}{2} + 3 = 4$

Step4: Equate exponents (same base)

$a^4 = a^x \implies x=4$
Final answer
x equals 4

$\sqrt{a} = a^\frac{1}{2}$

$a^\frac{1}{2} \cdot a^\frac{1}{2} \cdot a^3$

$\frac{1}{2} + \frac{1}{2} + 3 = 4$

$a^4 = a^x \implies x=4$

x equals 4

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Subject mathematics

Sub Subject algebra

Education Level high school

Difficulty unspecified

Question Type multiple choice, calculation

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-02-09T20:11:19

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solve the exponential equation $\\sqrt{a} \\cdot \\sqrt{a} \\cdot a^3 = a^x$ for x.
options:
x equals 3
x equals 2
x equals $\\frac{2}{3}$
x equals 4

mathematicsalgebramultiple choice, calculationhigh schoolturns-1

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