If b^(3)*(b^(4))^(2)=b^(x), what is the value of x ? Choose 1 answer: (A) 9 (B) 11 (C) 18 (D) 19

Simplify using properties of exponents: We need to simplify the left side of the equation using the properties of exponents. The property (b^(m))^n = b^(m*n) allows us to simplify (b^(4))^2.Apply property to simplify: Using the property, we get (b^(4))^2 = b^(4*2) = b^(8).Combine exponents: Now we have b^(3) * b^(8). Using the property of exponents that states b^(m) * b^(n) = b^(m+n), we can combine the exponents.Apply equality of exponents: Combining the exponents, we get b^(3+8) = b^(11).Determine the value of x: Now we have the equation b^(11) = b^(x). Since the bases are the same and the equation is an equality, the exponents must be equal.Therefore, x must be equal to 11.

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If
b^(3)*(b^(4))^(2)=b^(x), what is the value of
x ?
Choose 1 answer:
(A) 9
(B) 11
(C) 18
(D) 19

If $b^{3} \cdot\left(b^{4}\right)^{2}=b^{x}$ , what is the value of $x$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $9$ $\newline$ (B) $11$ $\newline$ (C) $18$ $\newline$ (D) $19$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. If

b^{3} \cdot\left(b^{4}\right)^{2}=b^{x}

, what is the value of

x

\newline

Choose

1

answer:

\newline

(A)

9

\newline

(B)

11

\newline

(C)

18

\newline

(D)

19

Simplify using properties of exponents: We need to simplify the left side of the equation using the properties of exponents. The property $(b^{m})^{n} = b^{m*n}$ allows us to simplify $(b^{4})^{2}$ .
Apply property to simplify: Using the property, we get $(b^{4})^{2} = b^{4\times2} = b^{8}$ .
Combine exponents: Now we have $b^{3} * b^{8}$ . Using the property of exponents that states $b^{m} * b^{n} = b^{m+n}$ , we can combine the exponents.
Apply equality of exponents: Combining the exponents, we get $b^{(3+8)} = b^{11}$ .
Determine the value of $x$ : Now we have the equation $b^{11} = b^{x}$ . Since the bases are the same and the equation is an equality, the exponents must be equal.
Determine the value of $x$ : Now we have the equation $b^{11} = b^{x}$ . Since the bases are the same and the equation is an equality, the exponents must be equal.Therefore, $x$ must be equal to $11$ .