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Yanka [14]
3 years ago
14

Simplify  ( √ 5 ) ( 3 √ 5 )

Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
8 0

Answer:

5^\frac{5}{6}

Step-by-step explanation:

\sqrt{5} can be represented as 5^{\frac{1}{2}} and \sqrt[3]5} can be represented as 5^{\frac{1}{3}}. Therefore, the expression can be rewritten as:

5^{\frac{1}{2}}*5^{\frac{1}{3}}

The rule for multiplying two exponents with the same base is you add the exponents. For example: x^m*x^k=x^{m+k}

We can use the same property to get:

5^{\frac{1}{2} +\frac{1}{3}}

which is just 5^\frac{5}{6} after you add the fractions

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<span>t < –5 and t may be a negative number!</span>
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Just number 7 would be fine but if you could also number 8 would help a lot​
BlackZzzverrR [31]

Answer:

7. r = -5

8. x = -1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

r + 2 - 8r = -3 - 8r

<u>Step 2: Solve for </u><em><u>r</u></em>

  1. Combine like terms:                    -7r + 2 = -3 - 8r
  2. Add 8r to both sides:                   r + 2 = -3
  3. Subtract 2 on both sides:            r = -5

<u>Step 3: Check</u>

<em>Plug in r into the original equation to verify it's a solution.</em>

  1. Substitute in <em>r</em>:                    -5 + 2 - 8(-5) = -3 - 8(-5)
  2. Multiply:                              -5 + 2 + 40 = -3 + 40
  3. Add:                                    -3 + 40 = -3 + 40
  4. Add:                                    37 = 37

Here we see that 37 does indeed equal 37.

∴ r = -5 is a solution of the equation.

<u>Step 4: Define equation</u>

-4x = x + 5

<u>Step 5: Solve for </u><em><u>x</u></em>

  1. Subtract <em>x</em> on both sides:                    -5x = 5
  2. Divide -5 on both sides:                      x = -1

<u>Step 6: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    -4(-1) = -1 + 5
  2. Multiply:                               4 = -1 + 5
  3. Add:                                     4 = 4

Here we see that 4 does indeed equal 4.

∴ x = -1 is a solution of the equation.

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