EXPONENTS AND ROOTS
Exponents are the small raised numbers written to the right of a variable or number. They indicate the number of times that variable
or number is to be used as a factor. On the SHSAT, you’ll usually deal with numbers or variables that are squared, but you could see
a few other concepts involving exponents.
To add or subtract terms consisting of a coefficient (the number in front of the variable) multiplied by a power (a power is a base
raised to an exponent), both the base and the exponent must be the same. As long as the base and the exponents are the same, you can
add the coefficients.
To multiply terms consisting of coefficients multiplied by powers having the same base, multiply the coefficients and add the
exponents.
MULTIPLYING POWERS
To multiply powers with the same base, add exponents. To raise a power to an exponent, multiply exponents.To divide terms consisting of coefficients multiplied by powers having the same base, divide the coefficients and subtract the
exponents.
To raise a power to an exponent, multiply the exponents.
A square root is a number that, when multiplied by itself, produces the given quantity. The radical sign “ ” is used to represent
the positive square root of a number, so , since 5 × 5 = 25.
PERFECT SQUARE
2 x^5 × 8x^7 = (2 × 8)(x5 + 7) = 16x^126 x^7 ÷ 2x^5 = (6 ÷ 2)(x7 − 5) = 3x^2(x^2 )^4 = x2 × 4 = x^8