Please help i put brainliest

Mathematics

1 answer:

valkas [14]2 years ago

4 0

Answer:

Step-by-step explanation:

x 12x - 6 3x + 3 6(2x - 1)

1 6 6 6

2 18 9 18

3 30 12 30

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Simplify the following expression. 7^-5/6.7^-7/6. 1/49 1/14 14 49

Serggg [28]

${7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } \\ = {7}^{ - \frac{5}{6} - \frac{7}{6} } \\ = {7}^{ - \frac{12}{6} } \\ = {7}^{ - 2} \\ = \frac{1}{ {7}^{2} } \\ = \frac{1}{49}$
The answer is 1/49

4 0

3 years ago

Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$