Find x so that ( - 7 ) x + 2 × ( - 7 ) 5 = ( - 7 ) 10 .

Given, ( - 7 ) x + 2 × ( - 7 ) 5 = ( - 7 ) 10 We have to find the value of x in given expression. Using the law of exponents, a n × a m = a n + m Now, ( - 7 ) x + 2 × ( - 7 ) 5 = ( - 7 ) 10 ( - 7 ) x + 2 + 5 = ( - 7 ) 10 Since the bases are equal, we equate the exponents to get ⇒ x + 7 = 10 ⇒ x = 10 - 7 ⇒ x = 3 Hence, the value of x is 3 .

Combine the scientific notations: 7 × 10 2 5 . 2 × 10 7

Given, 7 × 10 2 × 5 . 2 × 10 7 Standard form is used to express very small and very large numbers in a compact and efficient way. Each time you multiply a number by 10 each digit within the number moves one place order to the left. Any large number can be expressed in standard form by writing it as a number between 1 and 10 multiplied by a suitable power of 10 . Simplify the given expression by putting like terms together. ⇒ 7 × 10 2 × 5 . 2 × 10 7 ⇒ ( 7 × 5 . 2 ) × ( 10 2 × 10 7 ) Use the law of indices : a x × a y = a x + y ⇒ 36 . 4 × 10 9 The answer is numerically correct, but it is not in standard form because it's not lies between 1 & 10 . We can change it to standard by taking 3 . 64 × 10 1 . ⇒ 3 . 64 × 10 1 × 10 9 ⇒ 3 . 64 × 10 10 Therefore, the required answer is 3 . 64 × 10 10 .

Combine the scientific notations: 3 . 7 × 10 - 5 2 × 10 - 3

Given, 3 . 7 × 10 - 5 × 2 × 10 - 3 Standard form is used to express very small and very large numbers in a compact and efficient way. Each time you multiply a number by 10 each digit within the number moves one place order to the left. Any large number can be expressed in standard form by writing it as a number between 1 and 10 multiplied by a suitable power of 10 . Simplify the given expression by putting like terms together. ⇒ 3 . 7 × 10 - 5 × 2 × 10 - 3 ⇒ 3 . 7 × 2 × 10 - 5 × 10 - 3 Use the law of indices : a x × a y = a x + y ⇒ 7 . 4 × 10 - 8 Therefore, the required answer is 7 . 4 × 10 - 8 .