Properties of Exponents - SSAT Upper Level Quantitative

A power raised to a power indicates that you multiply the two powers.

$(3^{3}$$)^{2}$$=3^{3cdot 2}$$=3^{6}$

If you divide two exponential expressions with the same base, you can simply subtract the exponents. Here, both the top and the bottom have a base of 2 raised to a power.

So $$\frac{2^{10}$$$}{2^{8}$$}=2^{10-8}$$=2^{2}$=4

Since the two expressions have the same base, we just add the exponents.

$2^{3}$cdot $2^{2}$$=2^{3+2}$$=2^{5}$=32

We can either write 0.5times 0.5, or we can convert this to a fraction and write

$\frac{1}{2}$times $\frac{1}{2}$

$\frac{1}{2}$times $\frac{1}{2}$=\frac{1times 1}{2times 2}$=\frac{1}{4}$

$\frac{1}{4}$ in decimal form is 0.25.

$\sqrt{25}$=5

$\sqrt{36}$=6

34 is between 25 and 36, thus its square root must be between the square roots of 25 and 36. x must be a number between 5 and 6.

Convert .75 to a fraction. $\frac{75}{100}$=\frac{3}{4}$.

Now multiply $\frac{3}{4}$times $\frac{3}{4}$=\frac{3times 3}{4times 4}$=\frac{9}{16}$

If is odd, then , the sum of three odd integers, is odd; an odd number taken to any positive integer power is odd.

If is even, then , the sum of two odd integers and an even integer, is even; an even number taken to any positive integer power is even.

Therefore, always assumes the same odd/even parity as .

To rewrite a very small number in scientific notation:

Write the number.

Move the decimal point right as many places as needed until it follows the first nonzero digit, which here is the nine. Count the number of places it is moved - here it will be thirteen places.

The number formed is , which will be placed in front; , the negative of the number of places counted, will be the exponent. The number, in scientific notation, will be .

Therefore,

To solve this problem, we start with the parentheses and exponents in the denominator.

Next, we can bring the from the denominator up to the numerator by making the exponent negative.

Finally, to get rid of the negative exponent we can bring it back down to the denominator.

This is an undefined quantity.

as 0 taken to any positive power is equal to 0.

Any nonzero expression to the power of zero is equal to 1:

Applying the power of a product property of exponents, then the power of a power property:

This is not in scientific notation, so we adjust it as follows, applying the product of powers property:

Since any nonzero expression taken to the power of 0 is equal to 1,

Using the power of a product property of exponents, this becomes

Apply the product of powers property:

Since this is not in scientific notation, adjust as follows:

Rewriting the numerator and applying the quotient of powers property:

Since this is not in scientific notation, adjust as follows:

Rewriting the numeator and applying the quotient of powers property:

This is not in scientific notation, so we adjust it as follows, applying the product of powers property: