en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ye^{-2x}(ye^x)^3

Solution

simplify

y e^{- 2 x} (y e^{x})^{3}

Solution

e^{x} y^{4}

Solution steps

y e^{- 2 x} (y e^{x})^{3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2 x}} y (e^{x} y)^{3}

(y e^{x})^{3} : y^{3} e^{3 x}

= y \frac{1}{e ^{2 x}} y^{3} e^{3 x}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

y y^{3} = y^{1 + 3}

= \frac{1}{e ^{2 x}} y^{1 + 3} e^{3 x}

Add the numbers:

1 + 3 = 4

= \frac{1}{e ^{2 x}} y^{4} e^{3 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot y ^{4} e ^{3 x}}{e ^{2 x}}

Multiply:

1 \cdot y^{4} = y^{4}

= \frac{e ^{3 x} y ^{4}}{e ^{2 x}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{3 x}}{e ^{2 x}} = e^{3 x - 2 x} = e^{x}

= e^{x} y^{4}

Popular Examples

simplify (4sqrt(5))(4sqrt(5))simplify

(45) (45)

simplify 5.2x10^{-10}simplify

5.2 x 1 0^{- 10}

simplify 1.7*10^{-8}*e^{0.0039(-27-20)}simplify

1.7 \cdot 1 0^{- 8} \cdot e^{0.0039 (- 27 - 20)}

simplify \sqrt[3]{sqrt(81)}simplify

simplify e^{-3ln(cos(x))}simplify

e^{- 3 l n (c o s (x))}

Frequently Asked Questions (FAQ)

What is ye^{-2x}(ye^x)^3 ?
The solution to ye^{-2x}(ye^x)^3 is e^xy^4