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nadya68 [22]
2 years ago
10

Four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true

Mathematics
2 answers:
tiny-mole [99]2 years ago
6 0

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

(x^2)^?=x^4 \cdot x^8

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

\implies (x^2)^y=x^4 \cdot x^8

First, simplify the equation by applying exponent rules to either side of the equation:

\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:

\implies (x^2)^y=x^4 \cdot x^8

\implies x^{2y}=x^4 \cdot x^8

\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:

\implies x^{2y}=x^4 \cdot x^8

\implies x^{2y}=x^{4+8}

\implies x^{2y}=x^{12}

Now, apply the exponent rule:

x^{f(x)}=x^{g(x)} \implies f(x)=g(x)

Therefore,

x^{2y}=x^{12}\implies 2y=12

Finally, solve for y:

\implies 2y=12

\implies 2y \div 2 = 12 \div 2

\implies y=6

Therefore, <u>Joe is correct</u> as the unknown number is 6.

Feliz [49]2 years ago
5 0

Let's solve ourselves instead of believing anyone

\\ \rm\Rrightarrow (x^2)^7=x^4x^8

  • a^m+a^n=a^m+n

\\ \rm\Rrightarrow x^{14}=x^{4+8}

\\ \rm\Rrightarrow x^{14}=x^{12}

\\ \rm\Rrightarrow x^{14}-x^{12}=0

\\ \rm\Rrightarrow x^{12}(x^2-1)=0

\\ \rm\Rrightarrow x^2-1=0

\\ \rm\Rrightarrow x^2=1

\\ \rm\Rrightarrow x=\pm 1

  • 0 is also a solution
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