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High School Math : How to do exponents in pre-algebra

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Example Question #1 : How To Do Exponents In Pre Algebra

$Y^{3}\ast Y^{2}=?$

Possible Answers:

$Y^{4}$

$Y^{2}$

$Y^{6}$

$Y^{5}$

Correct answer:

$Y^{5}$

Explanation:

When you multiply exponents you can simply add the exponents:

$Y^{3}\ast Y^{2}=Y^{\left ( 3+2\right )}=Y^{5}$

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Example Question #2 : How To Do Exponents In Pre Algebra

Evaluate the exponential expression.

$\small (2^3)^2$

Possible Answers:

128

Correct answer:

Explanation:

We can solve this problem in two different ways.

The first way is to evaluate the internal term, $\small 2^3$ , and then square it.

$\small (2^3)^2=(2*2*2)^2=(8)^2$

$\small 8^2=64$

The second method is to use the power rule of exponents, where we multiply the exponents and solve the resulting term.

$(x^a)^b=x^{a*b}$

$\small (2^3)^2=2^{3*2}=2^6=64$

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Example Question #3 : How To Do Exponents In Pre Algebra

Evaluate $\dpi{100} \dpi{100} 9^{-\frac{1}{2}}$ .

Possible Answers:

$-\frac{1}{3}$

$\sqrt{-3}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

The negative sign in the exponent indicates that in order to solve you should use the reciprocal of the integer.

$\dpi{100} 9^{-\frac{1}{2}}=\frac{1}{9^{\frac{1}{2}}}$

$\frac{1}{9^{\frac{1}{2}}}=\frac{1}{\sqrt{9}}$

$\rightarrow\frac{1}{3}$

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Example Question #4 : How To Do Exponents In Pre Algebra

Evaluate $\dpi{100} (5^\frac{1}{2})^{2}$

Possible Answers:

$\sqrt{5}$

$5^{4}$

$\frac{1}{\sqrt{5}}$

$5^{2}$

Correct answer:

Explanation:

The laws of exponents state that when a number is raised to a certain power and then raised to another power then the exponents are multiplied by one another.

$(5^\frac{1}{2})^{2}=5^{(\frac{1}{2}*2)}$

Solve for the exponents.

$(\frac{1}{2}*2)=\frac{1}{2}*\frac{2}{1}$

$\rightarrow \frac{2}{2}\rightarrow1$

Therefore,

$\dpi{100} \dpi{100} (5^\frac{1}{2})^{2}=5^{1}$

$\rightarrow 5$

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Example Question #5 : How To Do Exponents In Pre Algebra

What is $2^{5}=?$

Possible Answers:

Correct answer:

Explanation:

When a number is raised to a power it means that the number is multiplied by itself the same number of times as the number of the power.

In this case is raised to the 5th power so it is equivalent to 2*2*2*2*2

We then perform the necessary multiplication to arrive at the answer of .

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Example Question #6 : How To Do Exponents In Pre Algebra

$4^{4}=?$

Possible Answers:

256

Correct answer:

256

Explanation:

When a number is raised to a power it means that the number is multiplied by itself the same number of times as the number of the power.

In this case is raised to the 4th power so it is equivalent to 4*4*4*4

We then perform the necessary multiplication to arrive at the answer of 256 .

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Example Question #7 : How To Do Exponents In Pre Algebra

Convert to standard notation.

$3.67\times 10^{-4}$

Possible Answers:

0.0000367

3,670,000

36,700

0.000367

Correct answer:

0.000367

Explanation:

Because the exponent is negative, we have to move the decimal four places to the left. We need to add three zeroes between the decimal the number three.

$3.67\rightarrow 0.000367$

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Example Question #8 : How To Do Exponents In Pre Algebra

Simplify the fractional expression.

$\frac{x^5}{x^2}$

Possible Answers:

x^1^0

x^2^.^5

$x^{-3}$

x^7

x^3

Correct answer:

x^3

Explanation:

Simplifying exponents with a common base can be done by subtracting the exponent in the denominator from the exponent in the numerator.

$\frac{x^5}{x^2}$

$x^{5-2}$

This gives us the final answer, x^3 .

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Example Question #9 : How To Do Exponents In Pre Algebra

Evaluate the term.

$5^{-2}$

Possible Answers:

$\frac{1}{25}$

Correct answer:

$\frac{1}{25}$

Explanation:

$5^{-2}$

A negative exponent can be written as a positive exponent in the denominator of a fraction.

$\frac{1}{5^2}$

Now we can evaluate the exponent and simplify.

$\frac{1}{25}$

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Example Question #10 : How To Do Exponents In Pre Algebra

What is 2^3 ?

Possible Answers:

$\sqrt{2}$

Correct answer:

Explanation:

When you see an exponent, remember it just means the number times itself that many times. That means that 2^3 is just another way to write 2*2*2 .

From here, we can solve it all together in a calculator, or do it in pieces on our own.

2^3=2*2*2

2^3=4*2

2^3=8

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High School Math : How to do exponents in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Do Exponents In Pre Algebra

Example Question #2 : How To Do Exponents In Pre Algebra

Example Question #3 : How To Do Exponents In Pre Algebra

Example Question #4 : How To Do Exponents In Pre Algebra

Example Question #5 : How To Do Exponents In Pre Algebra

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