Exponents - ACT Math

A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.

In equation , is the real component and is the imaginary component (designated by ).

In equation , is the real component and is the imaginary component.

When added,

A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.

First, distribute:

Then, group the real and imaginary components:

Solve to get:

When adding or subtracting complex numbers, the real terms are additive/subtractive, and so are the nonreal terms.

Complex numbers take the form a + bi, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number. Taking this, we can see that for the real number 8, we can rewrite the number as , where represents the (zero-sum) non-real portion of the complex number.

Thus, any real number can be added to any complex number simply by considering the nonreal portion of the number to be .

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Thus, to balance the equation, add like terms on the left side.

h–2n = 1/h2n

hn + h–2n = hn + 1/h2n

You multiply the integers, then add the exponents on the x's, giving you 24_x_5.

When multiplying exponents you smiply add the exponents.

For 2_x_² times 3_x_, 2 times 3 is 6, and 2 + 1 is 3, so 2_x_² times 3_x_ = 6_x_3

Using the rules of exponents, 23 + 22 = 8 + 4 = 12

The only value of x where the two equations equal each other is 1. All you have to do is substitute the answer choices in for x.

Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

Multiplying the two numbers yields 1080. Expressed in scientific notation 1080 is 1.08 x 103.

When common variables have exponents that are multiplied, their exponents are added. So _K_3 * _K_4 =K(3+4) = _K_7. And _M_6 * _M_2 = M(6+2) = _M_8. So the answer is _K_7/_M_8.

Add the coefficients of similar variables (y, y2, 9y3)

3y2 + 7y2 + 9y3 – y3 + y =

(3 + 7)y2 + (9 – 1)y3 + y =

10y2 + 8y3 + y

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

We now know that the exponents must be equal, and can solve for .

First, reduce all values to a common base using properties of exponents.

Plugging back into the equation-

Using the formula

We can reduce our equation to

So,

The rule for adding exponents is . We can thus see that and are no more compatible for addition than and are.

You could combine the first two terms into , but note that PEMDAS prevents us from equating this to (the exponent must solve before the distribution).

Since the problem requires us to finish in a power of 2, it's easiest to begin by reducing all terms to powers of 2. Fortunately, we do not need to use logarithms to do so here.

Thus,