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nataly862011 [7]

2 years ago

6

Which equation is equivalent to 2^4x = 8^x-3

2 answers:

Masteriza [31]2 years ago

8 0

Answer:2^4x = 8^x-3

Step-by-step explanation:Answer is D

VLD [36.1K]2 years ago

5 0

Answer:

<h2>x = -9</h2>

Step-by-step explanation:

$8=2^3\\\\8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\8^{x-3}=2^{3(x-3)}\qquad\text{use the distribtutive property}\ a(b+c)=ab+ac\\\\8^{x-3}=2^{3x-9}\\\\\text{Therefore}\\\\2^{4x}=8^{x-3}\Rightarrow2^{4x}=2^{3x-9}\iff4x=3x-9\qquad\text{subtract}\ 3x\ \text{from both isdes}\\\\4x-3x=3x-3x-9\\\\x=-9$

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. Express each exponent in expanded form: StartFraction 6 times 6 times 6 times 6 times 6 times 6 times 6 Over 6 times 6 times 6

vovangra [49]

Answer:

The exponent of the simplified power is 3

Step-by-step explanation:

Given:

6 × 6 × 6 × 6 × 6 × 6 × 6 / 6 × 6 × 6 × 6

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2 years ago

Which expressions are equivalent to R16? Check all that apply.

Ilya [14]

Option C: $(6^{-4})^{-4}$

Option D: $(6^{-2})^{-8}$

Option F: $(6^8)^2$

Solution:

Given expression: $6^{16}$

To find which expression is equivalent to the given expression.

Let us solve this using exponent rule: $\left(a^{b}\right)^{c}=a^{b c}$

Option A: $(6^{0})^{16}$

$(6^{0})^{16}=6^{0 \times 16}= 6^0$

It is not equivalent expression.

Option B: $(6^8)^8$

$(6^{8})^{8}=6^{8 \times 8}= 6^{64}$

It is not equivalent expression.

Option C: $(6^{-4})^{-4}$

$(6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}$

It is equivalent expression for the given expression.

Option D: $(6^{-2})^{-8}$

$(6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}$

It is equivalent expression for the given expression.

Option E: $(6^{-1})^{16}$

$(6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}$

It is not equivalent expression.

Option F: $(6^8)^2$

$(6^{8})^{2}=6^{8 \times 2}= 6^{16}$

It is equivalent expression for the given expression.

Hence $(6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2$ are the equivalent expressions.

Option C, Option D and Option F are correct answers.

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