Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

varsity tutors app store varsity tutors android store

Example Questions

Example Question #271 : Exponents

Simplify:  \(\displaystyle -2^6+2^3\)

Possible Answers:

\(\displaystyle 56\)

\(\displaystyle -56\)

\(\displaystyle -72\)

\(\displaystyle 20\)

\(\displaystyle 72\)

Correct answer:

\(\displaystyle -56\)

Explanation:

A number raised by a power is multiplied by itself that number of times.

Rewrite the expression.

\(\displaystyle -2^6+2^3 = -(2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2)+(2\cdot 2\cdot 2)\)

Simplify the terms.

\(\displaystyle -64+8 = -56\)

The answer is:  \(\displaystyle -56\)

Example Question #272 : Exponents

Simplify:  \(\displaystyle -2^3+0^1+3^2+5^2\)

Possible Answers:

\(\displaystyle 42\)

\(\displaystyle 27\)

\(\displaystyle 25\)

\(\displaystyle 26\)

\(\displaystyle 43\)

Correct answer:

\(\displaystyle 26\)

Explanation:

Evaluate each term.

\(\displaystyle -2^3 = -(2\times 2\times 2) = -8\)

\(\displaystyle 0^1=0\)

\(\displaystyle 3^2=9\)

\(\displaystyle 5^2 = 5\times 5 = 25\)

Add all the terms.

\(\displaystyle -8+9+25 = 26\)

The answer is:  \(\displaystyle 26\)

Example Question #273 : Exponents

Solve the exponents:  \(\displaystyle 4^2+5^3-(-2)^3\)

Possible Answers:

\(\displaystyle 37\)

\(\displaystyle 133\)

\(\displaystyle 141\)

\(\displaystyle 29\)

\(\displaystyle 149\)

Correct answer:

\(\displaystyle 149\)

Explanation:

Simplify each term.  An number raised to a certain integer is the number of times the number will multiply itself by.

\(\displaystyle 4^2 =4\times 4= 16\)

\(\displaystyle 5^3 = 5\times 5\times 5= 125\)

\(\displaystyle (-2)^3 = (-2)(-2)(-2) = -8\)

Determine the sum.

\(\displaystyle 4^2+5^3-(-2)^3 = 16+125-(-8) = 16+125+8 = 149\)

The answer is:  \(\displaystyle 149\)

Example Question #274 : Exponents

Solve:  \(\displaystyle 2^3+8^2-10^3\)

Possible Answers:

\(\displaystyle -6\)

\(\displaystyle -928\)

\(\displaystyle 34\)

\(\displaystyle -1019\)

\(\displaystyle -978\)

Correct answer:

\(\displaystyle -928\)

Explanation:

Evaluate each term given.

\(\displaystyle 2^3=8\)

\(\displaystyle 8^2=64\)

\(\displaystyle 10^3= 1000\)

Rewrite the expression.

\(\displaystyle 2^3+8^2-10^3=8+64-1000 =-928\)

The answer is:  \(\displaystyle -928\)

Example Question #271 : Exponents

Evaluate: \(\displaystyle (-9)^4\)

Possible Answers:

\(\displaystyle -6561\)

\(\displaystyle 6561\)

\(\displaystyle 8451\)

\(\displaystyle 7241\)

\(\displaystyle -8451\)

Correct answer:

\(\displaystyle 6561\)

Explanation:

We know that \(\displaystyle (-9)^4=-9*-9*-9*-9\). The product is positive we have even number of negative signs. Therefor our answer is \(\displaystyle 6561\).

Example Question #272 : Exponents

Evaluate: \(\displaystyle -6^3\)

Possible Answers:

\(\displaystyle -216\)

\(\displaystyle -18\)

\(\displaystyle -162\)

\(\displaystyle 216\)

\(\displaystyle 64\)

Correct answer:

\(\displaystyle -216\)

Explanation:

We know that \(\displaystyle -6^3\) is expanded out to \(\displaystyle -(6*6*6)\). Remember we apply the exponent part of PEMDAS before we add the negative sign. Therefore our answer is \(\displaystyle -216\).

Example Question #273 : Exponents

Expand: \(\displaystyle 6^7\)

Possible Answers:

\(\displaystyle 6^7*6^7*6^7*6^7*6^7*6^7*6^7\)

\(\displaystyle 7*7*7*7*7*7\)

\(\displaystyle 6*6*6*6*6*6*6\)

\(\displaystyle 6*7*6*7*6*7\)

\(\displaystyle 7*6\)

Correct answer:

\(\displaystyle 6*6*6*6*6*6*6\)

Explanation:

To expand the exponent, we multiply the base by whatever the exponent is.

\(\displaystyle 6^7=6*6*6*6*6*6*6\)

Example Question #274 : Exponents

Expand: \(\displaystyle -5^7\)

Possible Answers:

\(\displaystyle -5*-5*-5*-5*-5*-5*-5\)

\(\displaystyle 5^7*5^7*5^7*5^7*5^7*5^7*5^7\)

\(\displaystyle -5^7*-5^7*-5^7*-5^7*-5^7*-5^7*-5^7\)

\(\displaystyle -(5*5*5*5*5*5*5)\)

\(\displaystyle -5*7\)

Correct answer:

\(\displaystyle -(5*5*5*5*5*5*5)\)

Explanation:

To expand the exponent, we multiply the base by whatever the exponent is. Because there is a negative sign present, we need to apply the exponent first and then add the negative sign.

\(\displaystyle -5^7=-(5*5*5*5*5*5*5)\)

Example Question #275 : Exponents

Expand: \(\displaystyle (-4^5)\)

Possible Answers:

\(\displaystyle -4*5\)

\(\displaystyle -4^5*-4^5*-4^5*-4^5*-4^5\)

\(\displaystyle -4*-4*-4*-4*-4\)

\(\displaystyle 4*4*4*4*4\)

\(\displaystyle -5*-5*-5*-5\)

Correct answer:

\(\displaystyle -4*-4*-4*-4*-4\)

Explanation:

To expand the exponent, we multiply the base by whatever the exponent is.

\(\displaystyle (-4^5)=-4*-4*-4*-4*-4\)

Example Question #276 : Exponents

Evaluate: \(\displaystyle \frac{3}{x^0+y^0}\)

Possible Answers:

undefined

\(\displaystyle \frac{3}{2}\)

\(\displaystyle \frac{2}{3}\)

\(\displaystyle \frac{3}{x+y}\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle \frac{3}{2}\)

Explanation:

Although we have two variables, we do know that a number raised to a zero power is one. Therefore:

\(\displaystyle \frac{3}{x^0+y^0}=\frac{3}{1+1}=\frac{3}{2}\)

Learning Tools by Varsity Tutors