If 8^((5)/(6))-8^((1)/(2))=8^(m) for some value of m, what is the value of m ? Choose 1 answer: (A) (1)/(3) (B) (1)/(2) (C) 1 (D) (5)/(3)

Question

If  8^((5)/(6))-8^((1)/(2))=8^(m) for some value of  m, what is the value of  m ? Choose 1 answer: (A)  (1)/(3) (B)  (1)/(2) (C) 1 (D)  (5)/(3)

Bytelearn · Accepted Answer

Recognize Base Property: Recognize that the base of all terms is 8, which allows us to use the properties of exponents to combine the terms.Rewrite Subtraction as Division: Rewrite the subtraction of the powers as a division of the same base using the property a^(m) - a^(n) = a^(m) / a^(n) when a > 0 and a ≠ 1. 8^(5/6) - 8^(1/2) = 8^(5/6) / 8^(1/2)Apply Exponent Property: Apply the property of exponents that states a^(m) / a^(n) = a^(m-n) to simplify the expression. 8^(5/6) / 8^(1/2) = 8^((5/6) - (1/2))Find Common Denominator: Find a common denominator to subtract the fractions (5/6) and (1/2). The common denominator is 6, so we rewrite (1/2) as (3/6). 8^((5/6) - (3/6))Subtract Fractions: Subtract the fractions. (5/6) - (3/6) = (2/6)Simplify Fraction: Simplify the fraction (2/6) to its lowest terms. (2/6) = (1/3)Write as Exponent: Write the simplified fraction as the exponent of 8. 8^(1/3)Final Expression: Recognize that 8^(1/3) is the final expression for 8^m, which means m = 1/3.

If $8^{\frac{5}{6}}-8^{\frac{1}{2}}=8^{m}$ for some value of $m$ , what is the value of $m$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{3}$ $\newline$ (B) $\frac{1}{2}$ $\newline$ (C) $1$ $\newline$ (D) $\frac{5}{3}$

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If 856−812=8m 8^{\frac{5}{6}}-8^{\frac{1}{2}}=8^{m} 865​−821​=8m for some value of m m m, what is the value of m m m ?\newlineChoose 111 answer:\newline(A) 13 \frac{1}{3} 31​\newline(B) 12 \frac{1}{2} 21​\newline(C) 111\newline(D) 53 \frac{5}{3} 35​

If $8^{\frac{5}{6}}-8^{\frac{1}{2}}=8^{m}$ for some value of $m$ , what is the value of $m$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{3}$ $\newline$ (B) $\frac{1}{2}$ $\newline$ (C) $1$ $\newline$ (D) $\frac{5}{3}$