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ISEE Middle Level Math : How to multiply variables

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Example Questions

Example Question #71 : Variables

Simplify the following statement

(14b^2t^5)(2b^3t^9)

Possible Answers:

$14b^5t^{14}$

$28b^5t^{14}$

$28b^4t^{4}$

$28t^5b^{14}$

Correct answer:

$28b^5t^{14}$

Explanation:

Simplify the following statement

(14b^2t^5)(2b^3t^9)

To multiply these terms, first multiply the 2 and the 14

28(b^2t^5)(b^3t^9)

Next, we can combine the b's and the t's by adding together their exponents.

$28(b^2t^5)(b^3t^9)=28b^5t^{14}$

So our answer is:

$28b^5t^{14}$

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Example Question #71 : Variables

Combine the following terms:

$5q^3*8q^4*9q^{11}$

Possible Answers:

$360q^{18}$

$360q^{7}$

$36q^{18}$

$360q^{12}$

Correct answer:

$360q^{18}$

Explanation:

Combine the following terms:

$5q^3*8q^4*9q^{11}$

Let's begin by multiplying the coefficients (numbers out in front)

5*8*9=40*9=360

So our answer must have 360 in front.

Next, let's multiply our q's. To do so, we need to add up our exponents.

$q^3*q^4*q^{11}=q^{3+4+11}=q^{18}$

So, put it together to get:

$360q^{18}$

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Example Question #72 : Variables

$x^{2} = 64$ . Evaluate $x^{4}$ .

Possible Answers:

512

4,096

Correct answer:

4,096

Explanation:

$x^{2} = 64$ , so either $x = \sqrt{64} = 8$ or $x = - \sqrt{64} =- 8$ .

If the former is true,

$x^{4} = 8^{4} = 8 \cdot 8 \cdot 8 \cdot 8 = 4,096$ .

If the latter is true, then, since an even-numbered power of any number is positive,

$x^{4} =( - 8)^{4} = 8^{4} = 4,096$ .

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Example Question #73 : Variables

Simplify the following expression

$54x^3*8x^2*\frac{x^2}{9}$

Possible Answers:

48x^7

$1244x^{12}$

540x^7

$48x^{12}$

Correct answer:

48x^7

Explanation:

Simplify the following expression

$54x^3*8x^2*\frac{x^2}{9}$

Let's begin by grouping our x's and our coefficients

$(54*8*\frac{1}{9})(x^3*x^2*x^2)$

We can combine our coefficents by multiplying them, and we can combine the x's by adding the exponents

$(54*\frac{1}{9}*8)(x^7)=(6*8)x^7=48x^7$

So, our answer is:

48x^7

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Example Question #71 : Operations

2a = 3b = 66

Evaluate .

Possible Answers:

121

676

726

Correct answer:

726

Explanation:

First, use the given equations to solve for both the individual variables.

2a = 66

$2a \div 2 = 66 \div 2$

a = 33

3b = 66

$3b \div 66 = 66\div 3$

b = 22

Now that both variables have been solved for, find their product.

$ab =22 \cdot 33 = 726$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to multiply variables

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #71 : Variables

Example Question #71 : Variables

Example Question #72 : Variables

Example Question #73 : Variables

Example Question #71 : Operations

All ISEE Middle Level Math Resources

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