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Radicals and rational exponents: foundations
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The equation
2^(c)*b^(c)=10^(c) is true for all values of
c. What is the value of b?

dvanced-math-easier/xOfcc $98$ a $58$ ba $3$ bea $7$ radicals-and-rational-exponents-easier/e/v $2$ -radicals-and-rational-ex $\newline$ Q $\newline$ Khan Academy $\newline$ Cet Al Tutoring $\newline$ NEW $\newline$ Radicals and rational exponents: foundations $\newline$ ■ Google Classroom $\newline$ The equation $2^{c} \cdot b^{c}=10^{c}$ is true for all values of $c$ . What is the value of b?

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Find recursive and explicit formulas

Full solution

Q. dvanced-math-easier/xOfcc

98

a

58

ba

3

bea

7

radicals-and-rational-exponents-easier/e/v

2

-radicals-and-rational-ex

\newline

Q

\newline

Khan Academy

\newline

Cet Al Tutoring

\newline

NEW

\newline

Radicals and rational exponents: foundations

\newline

■ Google Classroom

\newline

The equation

2^{c} \cdot b^{c}=10^{c}

is true for all values of

c

. What is the value of b?

Given Equation: We are given the equation $2^{c} \cdot b^{c} = 10^{c}$ . To find the value of $b$ , we need to isolate $b$ on one side of the equation.
Simplify Equation: Since the equation is true for all values of $c$ , we can simplify the equation by removing the exponent $c$ from all terms. This is possible because if $a^x \cdot b^x = c^x$ , then $a \cdot b = c$ .
Remove Exponent: We remove the exponent $c$ from all terms to get $2 \times b = 10$ .
Solve for b: Now, we solve for $b$ by dividing both sides of the equation by $2$ . $b = \frac{10}{2}$
Evaluate Division: Evaluating the division gives us the value of $b$ . $b = 5$

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