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)

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 exponents as the division of the same base with the exponents. 8^(5/6) - 8^(1/2) can be written as 8^(5/6) * 8^(-1/2) because subtracting exponents with the same base is equivalent to dividing them, which in turn is equivalent to multiplying by the reciprocal exponent.Add Exponents: Add the exponents since the bases are the same. 8^(5/6 + (-1/2)) = 8^(5/6 - 3/6) = 8^(2/6)Simplify Exponent: Simplify the exponent 2/6 to its lowest terms. 2/6 simplifies to 1/3.Write Simplified Exponent: Write the simplified exponent with the base. 8^(2/6) = 8^(1/3)Conclude Value of m: Conclude that the value of m is the simplified exponent. Therefore, m = 1/3.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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)

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) $\frac{5}{3}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. 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

\frac{1}{2}

\newline

(C)

1

\newline

(D)

\frac{5}{3}

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 exponents as the division of the same base with the exponents. $8^{\frac{5}{6}} - 8^{\frac{1}{2}}$ can be written as $8^{\frac{5}{6}} \times 8^{-\frac{1}{2}}$ because subtracting exponents with the same base is equivalent to dividing them, which in turn is equivalent to multiplying by the reciprocal exponent.
Add Exponents: Add the exponents since the bases are the same. $\newline$ $8^{\frac{5}{6} + \left(-\frac{1}{2}\right)} = 8^{\frac{5}{6} - \frac{3}{6}} = 8^{\frac{2}{6}}$
Simplify Exponent: Simplify the exponent $\frac{2}{6}$ to its lowest terms. $\newline$ $\frac{2}{6}$ simplifies to $\frac{1}{3}$ .
Write Simplified Exponent: Write the simplified exponent with the base. $8^{\frac{2}{6}} = 8^{\frac{1}{3}}$
Conclude Value of m: Conclude that the value of m is the simplified exponent. $\newline$ Therefore, $m = \frac{1}{3}$ .