Question

(A) simplify 3x^-2 (B) simplify 5x^2y(2x^4y^-3)

Answer 1

Answer:

A. $\frac{3}{x^2}$

B. $\frac{10x^6}{y^2}$

Step-by-step explanation:

A.

Our expression is: $3x^{-2}$, where we have a negative exponent.

Remember that negative exponents are the same as taking the reciprocal of the number and taking that to the positive exponent.

Here, we have $x^{-2}$, so its reciprocal is just 1/x. Now, we take the positive square of the reciprocal: $\frac{1}{x^2}$. Put the 3 in and our final answer is: $\frac{3}{x^2}$.

B.

Our expression is: $5x^2y(2x^4y^{-3})$. Basically, we're multiplying these together.

Remember that when multiplying numbers with the same base, we always add the exponents. Here, we have:

$5x^2y(2x^4y^{-3})=5*2*x^2y*x^4y^{-3}=10x^2y*x^4y^{-3}$

The two x terms will combine to become $x^{2+4}=x^6$, and the two y terms will combine to become $y^{1+(-3)}=y^{-2}=\frac{1}{y^2}$.

The final answer is: $\frac{10x^6}{y^2}$.

Answer 2

I’ll teach you solve 3x^-2 and 5x^2y(2x^4y^-3)

——————————————

(A)

3x^-2

Apply exponent rule:

3*1/x^2

Multiply fractions:

1*3/x^2

Multiply the numbers:

1*3= 3

3/x^2

Your Answer Is $\frac{3}{x^{2} }$

(B)

5x^2y(2x^4 y^-3)

Apply exponent rule:

5y*2x^2+4 y^-3

Add the numbers:

2+4= 6

5y*2x^6 y^-3

Apply exponent rule:

5*2x^6 y^1-3

Subtract the numbers:

1-3= -2

5*2x^6 y^-2

Apply exponent rule:

5*2* 1/y^2 x^6

Multiply fractions:

1*5*2x^6/y^2

Multiply the numbers:

1*5*2= 10

10x^6/y^2

Your Answer Is $\frac{10x^{6} }{y^{2} }$

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