8^(-(1)/(2))*8^((7)/(6)) What is the value of the given expression?

Apply exponent property: Apply the property of exponents that states when multiplying expressions with the same base, you add the exponents. 8^(-(1)/(2)) * 8^((7)/(6)) = 8^((-(1)/(2)) + (7)/(6))Add exponents: Add the exponents (-(1)/(2)) and (7)/(6) together. (-(1)/(2)) + (7)/(6) = (-3)/(6) + (7)/(6) = (4)/(6)Simplify the fraction: Simplify the fraction (4)/(6) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. (4)/(6) = (2*2)/(2*3) = (2)/(3)Substitute simplified exponent: Substitute the simplified exponent back into the base 8. 8^((4)/(6)) simplifies to 8^((2)/(3))Calculate value of 8^(2/3): Calculate the value of 8^((2)/(3)). Since 8 = 2^3, we can rewrite 8^((2)/(3)) as (2^3)^((2)/(3)). (2^3)^((2)/(3)) = 2^(3*(2)/(3)) = 2^2Calculate value of 2^2: Calculate the value of 2^2. 2^2 = 2 * 2 = 4

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8^(-(1)/(2))*8^((7)/(6))
What is the value of the given expression?

$8^{-\frac{1}{2}} \cdot 8^{\frac{7}{6}}$ $\newline$ What is the value of the given expression?

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Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

8^{-\frac{1}{2}} \cdot 8^{\frac{7}{6}}

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What is the value of the given expression?

Apply exponent property: Apply the property of exponents that states when multiplying expressions with the same base, you add the exponents. $\newline$ $8^{-(\frac{1}{2})} \times 8^{\frac{7}{6}} = 8^{\left(-(\frac{1}{2}) + \frac{7}{6}\right)}$
Add exponents: Add the exponents $\left(-\frac{1}{2}\right)$ and $\frac{7}{6}$ together. $\newline$ $\left(-\frac{1}{2}\right) + \frac{7}{6} = \left(-\frac{3}{6}\right) + \frac{7}{6} = \frac{4}{6}$
Simplify the fraction: Simplify the fraction $(4)/(6)$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $(4)/(6) = (2 \times 2)/(2 \times 3) = (2)/(3)$
Substitute simplified exponent: Substitute the simplified exponent back into the base $8$ . $8^{(4)/(6)}$ simplifies to $8^{(2)/(3)}$
Calculate value of $8^{\frac{2}{3}}$ : Calculate the value of $8^{\left(\frac{2}{3}\right)}$ . Since $8 = 2^3$ , we can rewrite $8^{\left(\frac{2}{3}\right)}$ as $(2^3)^{\left(\frac{2}{3}\right)}$ . $\newline$ $(2^3)^{\left(\frac{2}{3}\right)} = 2^{3\left(\frac{2}{3}\right)} = 2^2$
Calculate value of $2^2$ : Calculate the value of $2^2$ . $\newline$ $2^2 = 2 \times 2 = 4$